Melissa Zhang





Contact Information

Simons Laufer Mathematical Research Institute
17 Gauss Way
Berkeley, CA 94720-5070

she/her/hers



About me

I am currently a Viterbi Endowed Postdoctoral Fellow at MSRI/SLMath, in the Fall 2022 Floer Homotopy Theory semester program. Afterwards, I will join the Department of Mathematics at UC Davis as a Krener Assistant Professor. Previously, I was a Limited Term Assistant Professor in the Department of Mathematics at the University of Georgia. I received my PhD in 2019 from Boston College under the supervision of J. Elisenda Grigsby and David Treumann, and spent my fifth year as a Visiting PhD Student at Columbia University.

My research is in the field of low-dimensional topology, which for me means knots, links, and their relationships with 3- and 4-dimensional spaces, sometimes with extra geometric structure. I focus on connections between two families of homology-type invariants: quantum link homology theories and Floer theories. In particular, I construct and study analogues to algebraic constructions from Heegaard Floer homologies in Khovanov homologies, in order to explore the depths of geometric and topological information captured within quantum invariants. My exploration has led me to become interested in tools from homotopy theory, representation theory, combinatorics, symplectic/contact geometry, and more!

[CV, updated September 2022]

In Fall 2022, I am organizing a learning seminar at SLMath called [Homotopy Types in Low-Dimensional Topology]. Click on the link to visit the webpage containing resources for this seminar.

Publications

On Khovanov homology and related invariants
Carmen Caprau, Nicolle González, Christine Ruey Shan Lee, Adam M. Lowrance, Radmila Sazdanović, and Melissa Zhang
Proceedings Volume of the Research Collaboration Conference of the Women in Symplectic and Contact Geometry and Topology
[arXiv]

Annular link invariants from the Sarkar-Seed-Szabó spectral sequence
Linh Truong and Melissa Zhang
Michigan Mathematical Journal
[arXiv]

Localization in Khovanov homology
Matthew Stoffregen and Melissa Zhang
Accepted for publication in Geometry & Topology
[arXiv]

A rank inequality for the annular Khovanov homology of 2-periodic links
Melissa Zhang
Algebraic & Geometric Topology
[arXiv]



Preprints / In Preparation

Concordance invariants from U(1)xU(1)-equivariant Khovanov homology
Rostislav Akhmechet and Melissa Zhang
[arXiv]

Khovanov homology and the Involutive Heegaard Floer Homology of branched double covers
Akram Alishahi, Linh Truong, and Melissa Zhang

Code :
These are provided as .txt files; change the extension to .py.
Omega Merge Split



Lecture Series on Annular Khovanov Homology

In August 2021, I gave a series of four lectures at the Perspectives on quantum link homology theories workshop organized by Lukas Lewark and Claudius Zibrowius and hosted by the University of Regensburg.

Videos of the lectures are available on their website:
[Videos]

Lecture 1: Basics of annular Khovanov homology
[slides]

Lecture 2: AKh and periodic links
[slides]

Lecture 3: sl(2) action on AKh, annular Khovanov-Lee homology
[slides]

Lecture 4: A further sampling of applications of AKh
[slides]



[Teaching]

In my teaching, my first goal is to pique students' interest in the content, so that learning becomes a means to satisfy curiosity. In the classroom, I am currently focusing on active learning techniques, and like to give my students the time to think about questions — to ask and to answer — during our class meetings. I aim to support my students as a whole persons, as I recognize that everyone has unique struggles and needs which need to be resolved for learning to occur most efficiently.



Other Stuff



Family

My partner Alex Wein is also a mathematician.
My sister-in-law Nicole Wein is a theoretical computer scientist.
My sister-in-law Natasha Wein is an artist. She works wonders with resin too.
My sister-in-law² Maya Hladisova is a designer.



[Round Animals]

I've been painting a lot of round animals.

[Mathematical Riddles]

I'm slowly curating my favorite mathematical riddles.

[Puzzles for K.]

These are some puzzles I worked on with an awesome middle schooler during the first year of the pandemic.

[5-minute talk timer]

[3-second talk timer demo]



[Bulk-delete Watch Later Playlist]

Sometimes I don't want to watch the dregs of my "Watch later" playlist and just want to delete them. But YouTube doesn't give you an easy way to do this. You can use AutoIt to bulk-delete unwatched videos on your YouTube "Watch later" playlist.